Galliani has told Gazzetta dello Sport that he had to convince the Brazilian to take the job initially last summer.
"Leonardo was not going to coach AC Milan," revealed Galliani. "Last year, I convinced him, myself. And this year I'll convince him to stay beyond his two-year contract. I say that he will succeed.
"Does (patron) Silvio Berlusconi think the same? He would say the same.
"His criticism of Leonardo? The debates are routine, I do not know how many times you hear and see the same thing elsewhere."
Galliani also confirmed plans to bring former Milan captain Paolo Maldini back to the club.
"The relationship with Paolo is great. We're thinking about him. But everything will be decided in time."